La circunferencia es tangente a la recta 3x - 4y = 34 en el punto (10, -1) Y también es tangente a la recta 4x + 3y = 12 en el punto (3, O). Hallar la ecuación de la circnferencia.

Answer:

La ecuación del círculo en la forma es (x - 145/12)² + (y - 109/16)² = (545/48)²

Step-by-step explanation:

La información dada son;

La primera línea tangente al círculo en el punto (10, -1) = 3·x - 4·y = 34

La segunda línea tangente al círculo en el punto (3, 0) = 4·x + 3·y = 12

Las rectas tangentes dadas en forma de pendiente e intersección, y = m·x + c son;

3·x - 4·y = 34

4·y = 34 - 3·x

y = 34/4 - 3/4·x = 8.5 - 3/4·x

Primera tangente

y = 8.5 - 3/4·x

3·y = 12 - 4·x

y = 12/3 - 4/3·x = 4 - 4/3·x

Segunda tangente

y = 4 - 4/3·x

La recta de la ecuación de los radios es perpendicular a la tangente y se encuentra con la tangente en el punto de intersección con el círculo como sigue;

La primera ecuación radial tiene pendiente, m = 1/(-3/4) = 4/3

La ecuación en forma de punto y pendiente es y - (-1) = 4/3×(x - 10)

y = 4/3×(x - 10) - 1 = 4/3·x - 40/3 - 1 = 4/3·x - 43/3

Por tanto, la ecuación del primer radio es;

y = 4/3·x - 43/3

La segunda ecuación radial tiene pendiente, m = 1/(-4/3) = 3/4

La ecuación en forma de punto y pendiente es y - 0 = 3/4×(x - 3)

y = 3/4×(x - 3) = 3/4·x - 9/4

Por tanto, la ecuación del segundo radio es;

y = 3/4·x - 9/4

Los dos radios se encuentran en el centro dado como sigue;

4/3·x - 43/3 = 3/4·x - 9/4

4/3·x - 3/4·x  = 43/3 - 9/4

7/12·x = 145/12

x = 145/12

y = 3/4·x - 9/4 = 3/4·145/12 - 9/4 = 109/16

Las coordenadas del centro = (h, k) = (145/12, 109/16)

La longitud del radio, r = √((109/16 - 0)² + (145/12 - 3)²) = 545/48

La ecuación del círculo en la forma (x - h)² + (y - k)² = r² es, por lo tanto;

(x - 145/12)² + (y - 109/16)² = (545/48)².

i would really really appreciate some help on this... brainliest to whoever can help?..

Find the slope and the y-intercept of this table. X 0 3 6 9 and y 4 6 8 10 ​

20 POINTS!!
( Also explain the reasoning you used to find the value of P)
ILL MARK BRAINLIEST!!

if a triangular sail has a vertical height of 83 ft and horizantal length of 40 ft, what is the area of the sail?

Solve for x. 2/3(x−7)= −2
Enter your answer on the line.
x = __

In chemistry class, Bob recorded the volume of a liquid as 17.7 mL. The actual volume was 17.1 mL. Use the formula to find percent error of Bob's measurement to the nearest tenth of a percent.

Percent Error =
|Experimental Value − Actual Value|
Actual Value
× 100

What is the value of (3/4)3?

What operation is being done to the variable in the equation -5m = -40?

It's being multiplied by -5.
It's being divided by -5.
It's being multiplied by -40.
It's being divided by -40.

Write an equation for a line that passes through (0,0) and is parallel to a line that passes through (-5, 3) and (2, 1)​

Find the midpoint of segment AB if A(3, 2) and B(-1,4) Select one: O b (2, 1) O b. (1,3) O c. (2,6) O d. (2,3)​

Antonio has $74 to spend on video games. He buys one game for $46.90 and another game for $11. How much money will he have left over?

: Sara took her two children out to lunch. Sara ordered a cheeseburger that cost $5.00 and her two children ordered pasta that cost $2.10 each. There is 10% sales tax. Calculate the total cost of the meal.

The football team has a total of jerseys 20 There are 14 ​medium-sized jerseys. What percent of the jerseys are​ medium-sized jerseys?

Eliza claims she can create an equation using these cards that has NO solutions. Axel says this is impossible—that every equation created with these cards will have a solution. Who is right?

what is 3.14 times 5 divided by 7​

Round 25.395 to the nearest hundredths.

how many minutes are there in one monty​

Which equation below would be best solved by using the addition property of equally?
1-23-45
231-45
f. 23-45
1-23 - 45

Sam scored 10 points. This was double the number of points he scored in the first game. Which equation can be used to find, x, the number of points Sam scored in the first game?
a.x−2=10
b.2x = 10
c.x + 2 = 10
d.x/2=10

Fihding the Selling Price for a Given Profit
Soccer ball profit
y = -6x2 + 100x – 180
Suppose the store wants to earn a daily profit of
$150 from the sale of soccer balls. To earn this
profit, what price should the store charge for each
soccer ball? Explain how to solve this problem.
DONE
) Intro
6 of 8

question in the picture!!

looking for the answer of 3) and 4) !!

<3

A wire 45 meters long is cut into two pieces, One piece is 5 meters longer than the other. What is the length of the two pieces? Create an equation and solve .

URGENT PLEASE HELP PLEASE

Write the product of 7×2×7×2×7 in exponential form

0.612 as a simplified fraction ​

Find the slope of each line.
8x + y = 10

please help super soon my time is up in 5 minutes

10 divided by 2 would be 5 because it pretty much splits it in equal parts like this if you do each friend get 1 cup of water there is 9 liters so what you do it give each 3 liters of water and that's 9 divided by 3 so you split 3 parts into 9

1. The sum of two consecutive integers is 27. What are the two integers?|

11. Samuel's current salary is $30,000. He has been
promised a raise to $31,500 next year. His raise
will be what percent increase over his current
salary?
A. 3%
B. 3.5%
C. 4%
D. 5%

WILL GIVE BRAINLY
A trail begins at an elevation of –50 feet below sea level. The trail ends at an elevation of 287 feet above sea level. By how many feet does the elevation of the trail change from beginning to end? PLEASE EXPLAIN